Metallocenes and their use as catalysts in the polymerization of olefins have been known for a long time (EP-A 129 368 and the literature cited therein). It is furthermore known from EP-A '368 that metallocenes in combination with aluminum-alkyl/water as cocatalysts are active systems for the polymerization of ethylene (thus, for example, methylaluminoxane=MAO is formed from 1 mol of trimethylaluminum and 1 mol of water. Other stoichiometric ratios have also already been used successfully (WO 94/20506 )). Metallocenes in which the cyclopentadienyl skeletons are linked to one another covalently via a bridge are also already known. An example of the numerous patents and applications in this field which may be mentioned is EP-A 704 461, in which the linkage group mentioned therein is a (substituted) methylene group or ethylene group, a silylene group, a substituted silylene group, a substituted germylene group or a substituted phosphine group. The bridged metallocenes are also envisaged as polymerization catalysts for olefins in EP '461. In spite of the numerous patents and applications in this field, there continues to be a demand for improved catalysts which are distinguished by a high activity, so that the amount of catalyst remaining in the polymer can be set to a low level, and which are equally suitable for the polymerization and copolymerization of olefins to give thermoplastics and to give elastomeric products and also for the polymerization and copolymerization of diolefins, optionally with olefins.